Let's separate the warranty (as it's been mentioned here) from your statutory rights:
A warranty can be as generous or as limited as the manufacturer chooses. (It's a 'gift' that's entirely separate to the contract of purchase with the retailer). So if the manufacturer says that the guarantee is only valid for two years there's no way that you can challenge that decision.
Your statutory rights are based around the concept of an 'inherent fault'. i.e. something which was already wrong with the product at the time of purchase (such as the inclusion of poor quality components in the product). If a fault develops within the first SIX MONTHS after purchase, the law automatically assumes that it must have done so due to the the presence of an inherent fault (unless there's clear evidence to the contrary).
[Section 19(14) Consumer Rights act 2015]
Thereafter it's up to the purchaser to show that there was actually something wrong with the item at the time of purchase. (e.g. by paying for an independent report to prove that there was an 'inherent fault'). If he can't do so, then he has no further contractual rights, in respect of a repair or replacement, with the retailer.
The best line of attack can often be to ask the retailer to suggest why the machine could have failed for any reason other than due to the presence of an inherent fault. That might back him into a corner, forcing him to accept that only an inherent fault is likely to have been the cause of the problem. However the retailer isn't obliged to respond to your request for him to suggest the likely cause of the failure, so that approach won't always work.
Other than that, all you can do is to complain via social media (in the hope that either the retailer or the manufacturer will respond positively to the bad publicity) and/or seek the assistance of the press (e.g. you local newspaper or the consumer rights columnists in the national newspapers) to put the retailer and/or manufacturer under pressure to act.